{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03 - Stats Review: The Most Dangerous Equation\n",
    "\n",
    "In his famous article of 2007, Howard Wainer writes about very dangerous equations:\n",
    "\n",
    "\"Some equations  are  dangerous  if you  know them, and others are dangerous if you do not. The first category may  pose  danger  because the secrets  within its bounds open  doors  behind which lies terrible peril. The obvious winner in this is Einstein’s iconic equation $E = mc^2$, for it  provides  a  measure of  the  enormous energy hidden  within  ordinary  matter. \\[...\\] Instead I am interested in equations that unleash their danger not when we know about them, but rather when we do not. Kept close at hand, these equations allow us to understand things clearly, but their absence leaves us dangerously ignorant.\"\n",
    "\n",
    "The equation he talks about is Moivre’s equation:\n",
    "\n",
    "$\n",
    "SE = \\dfrac{\\sigma}{\\sqrt{n}} \n",
    "$\n",
    "\n",
    "where $SE$ is the standard error of the mean, $\\sigma$ is the standard deviation, and $n$ is the sample size. Sounds like a piece of math the brave and true should master, so let's get to it.\n",
    "\n",
    "To see why not knowing this equation is very dangerous, let's look at some education data. I've compiled data on ENEM scores (Brazilian standardised high school scores, similar to SAT) from different schools for 3 years. I also cleaned the data to keep only the information relevant to us. The original data can be downloaded on the [Inep website](http://portal.inep.gov.br/web/guest/microdados#).\n",
    "\n",
    "If we look at the top-performing school, something catches the eye: those schools have a reasonably small number of students. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use(\"fivethirtyeight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>school_id</th>\n",
       "      <th>number_of_students</th>\n",
       "      <th>avg_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16670</th>\n",
       "      <td>2007</td>\n",
       "      <td>33062633</td>\n",
       "      <td>68</td>\n",
       "      <td>82.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16796</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065403</td>\n",
       "      <td>172</td>\n",
       "      <td>82.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16668</th>\n",
       "      <td>2005</td>\n",
       "      <td>33062633</td>\n",
       "      <td>59</td>\n",
       "      <td>81.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16794</th>\n",
       "      <td>2005</td>\n",
       "      <td>33065403</td>\n",
       "      <td>177</td>\n",
       "      <td>81.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10043</th>\n",
       "      <td>2007</td>\n",
       "      <td>29342880</td>\n",
       "      <td>43</td>\n",
       "      <td>80.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18121</th>\n",
       "      <td>2007</td>\n",
       "      <td>33152314</td>\n",
       "      <td>14</td>\n",
       "      <td>79.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16781</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065250</td>\n",
       "      <td>80</td>\n",
       "      <td>79.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3026</th>\n",
       "      <td>2007</td>\n",
       "      <td>22025740</td>\n",
       "      <td>144</td>\n",
       "      <td>79.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14636</th>\n",
       "      <td>2007</td>\n",
       "      <td>31311723</td>\n",
       "      <td>222</td>\n",
       "      <td>79.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17318</th>\n",
       "      <td>2007</td>\n",
       "      <td>33087679</td>\n",
       "      <td>210</td>\n",
       "      <td>79.38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       year  school_id  number_of_students  avg_score\n",
       "16670  2007   33062633                  68      82.97\n",
       "16796  2007   33065403                 172      82.04\n",
       "16668  2005   33062633                  59      81.89\n",
       "16794  2005   33065403                 177      81.66\n",
       "10043  2007   29342880                  43      80.32\n",
       "18121  2007   33152314                  14      79.82\n",
       "16781  2007   33065250                  80      79.67\n",
       "3026   2007   22025740                 144      79.52\n",
       "14636  2007   31311723                 222      79.41\n",
       "17318  2007   33087679                 210      79.38"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"./data/enem_scores.csv\")\n",
    "df.sort_values(by=\"avg_score\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at it from another angle, we can separate only the 1% of top schools and study them. What are they like? Perhaps we can learn something from the best and replicate it elsewhere. And sure enough, if we look at the top 1% of schools, we figure out they have, on average, fewer students."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = (df\n",
    "             .assign(top_school = df[\"avg_score\"] >= np.quantile(df[\"avg_score\"], .99))\n",
    "             [[\"top_school\", \"number_of_students\"]]\n",
    "             .query(f\"number_of_students<{np.quantile(df['number_of_students'], .98)}\")) # remove outliers\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "sns.boxplot(x=\"top_school\", y=\"number_of_students\", data=plot_data)\n",
    "plt.title(\"Number of Students of 1% Top Schools (Right)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One natural conclusion is that small schools lead to higher academic performance. This makes intuitive sense since we believe that fewer students per teacher allow the teacher to give focused attention to each student. But what does this have to do with Moivre’s equation? And why is it dangerous? \n",
    "\n",
    "Well, it becomes dangerous once people start to make important and expensive decisions based on this information. In his article, Howard continues:\n",
    "\n",
    "\"In the 1990s, it became popular to champion reductions in the size of schools. Numerous philanthropic organisations and government agencies funded the division of larger schools because students at small schools are overrepresented in groups with high test scores.\"\n",
    "\n",
    "What people forgot to do was to look also at the bottom 1% of schools. If we do that, lo and behold! They also have very few students!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_99 = np.quantile(df[\"avg_score\"], .99)\n",
    "q_01 = np.quantile(df[\"avg_score\"], .01)\n",
    "\n",
    "plot_data = (df\n",
    "             .sample(10000)\n",
    "             .assign(Group = lambda d: np.select([d[\"avg_score\"] > q_99, d[\"avg_score\"] < q_01],\n",
    "                                                 [\"Top\", \"Bottom\"], \"Middle\")))\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", hue=\"Group\", data=plot_data)\n",
    "plt.title(\"ENEM Score by Number of Students in the School\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are seeing above precisely what is expected according to the Moivre’s equation. As the number of students grows, the average score becomes more and more precise. Schools with very few samples can have very high and low scores simply due to chance. This is less likely to occur in large schools. Moivre’s equation talks about a fundamental fact about the reality of information and records in the form of data: it is always imprecise. The question then becomes how inaccurate.\n",
    "\n",
    "Statistics is the science that deals with these imprecisions, so they don't catch us off-guard. As Taleb puts it in his book, Fooled by Randomness:\n",
    "\n",
    "> Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance.\n",
    "\n",
    "One way to quantify our uncertainty is the **variance of our estimates**. Variance tells us how much observation deviates from its central and most probable value. As Moivre’s equation indicates, this uncertainty shrinks as the amount of data we observe increases. This makes sense, right? If we see many students performing excellently at a school, we can be more confident that this is indeed a good school. However, if we see a school with only 10 students and 8 of them perform well, we need to be more suspicious. By chance, it could be that the school got some above-average students.\n",
    "\n",
    "The beautiful triangular plot we see above tells precisely this story. It shows us how our estimates of the school performance have a huge variance when the sample sizes are small. It also indicates that variance shrinks as the sample size increases. This is true for the average score in a school, but it is also true about any summary statistics we have, including the ATE we often want to estimate.\n",
    "\n",
    "##  The Standard Error of Our Estimates\n",
    "\n",
    "Since this is just a review of statistics, I'll take the liberty to go a bit faster now. If you are not familiar with distributions, variance, and standard errors, please read on, but keep in mind that you might need some additional resources. I suggest you google any MIT course on introduction to statistics. They are usually quite good.\n",
    "\n",
    "In the previous section, we estimated the average treatment effect $E[Y_1-Y_0]$ as the difference in the means between the treated and the untreated $E[Y|T=1]-E[Y|T=0]$. We figured out the $ATE$ for online classes as our motivating example. We also saw a negative impact; online classes made students perform about 5 points worse than the students with face-to-face classes. Now, we get to see if this impact is statistically significant.\n",
    "\n",
    "To do so, we need to estimate the $SE$. We already have $n$, our sample size. To get the estimate for the standard deviation, we can do the following\n",
    "\n",
    "$$\n",
    "\\hat{\\sigma}=\\sqrt{\\frac{1}{N-1}\\sum_{i=1}^N (x_i-\\bar{x})^2}\n",
    "$$\n",
    "\n",
    "where $\\bar{x}$ is the mean of $x$. Fortunately for us, most programming software already implements this. In Pandas, we can use the method [std](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.std.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE for Online: 1.5371593973041635\n",
      "SE for Face to Face: 0.8723511456319106\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/online_classroom.csv\")\n",
    "online = data.query(\"format_ol==1\")[\"falsexam\"]\n",
    "face_to_face = data.query(\"format_ol==0 & format_blended==0\")[\"falsexam\"]\n",
    "\n",
    "def se(y: pd.Series):\n",
    "    return y.std() / np.sqrt(len(y))\n",
    "\n",
    "print(\"SE for Online:\", se(online))\n",
    "print(\"SE for Face to Face:\", se(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence Intervals\n",
    "\n",
    "The standard error of our estimate is a measure of confidence. We need to go into turbulent and polemic statistical waters to understand precisely what it means. For one view of statistics, the frequentist view, we would say that our data is nothing more than a manifestation of an accurate data-generating process. This process is abstract and ideal. It is governed by true parameters that are unchanging but also unknown to us. In the context of the students' test, if we could run multiple experiments and collect multiple datasets, all would resemble the true underlying data generating process but wouldn't be exactly like it. This is very much like Plato's writing on the Forms:\n",
    "\n",
    "> Each [of the essential forms] manifests itself in a great variety of combinations, with actions, with material things, and with one another, and each seems to be many\n",
    "\n",
    "Let's suppose we have a true abstract distribution of students' test scores to better grasp this. This is a normal distribution with a true mean of 74 and a true standard deviation of 2. From this distribution, we can run 10000 experiments. On each one, we collect 500 samples. If we plot them in a histogram, we can see that means of the experiments are distributed around the true mean. Some experiment data will have a mean lower than the true one, and some will be higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_std = 2\n",
    "true_mean = 74\n",
    "\n",
    "n = 500\n",
    "def run_experiment(): \n",
    "    return np.random.normal(true_mean,true_std, 500)\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "freq, bins, img = plt.hist([run_experiment().mean() for _ in range(10000)], bins=40, label=\"Experiment Means\")\n",
    "plt.vlines(true_mean, ymin=0, ymax=freq.max(), linestyles=\"dashed\", label=\"True Mean\", color=\"orange\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we are talking about the mean of means here. So, by chance, we could have an experiment where the mean is somewhat below or above the true mean. This is to say that we can never be sure that the mean of our experiment matches the true platonic and ideal mean. However, **with the standard error, we can create an interval that will contain the true mean 95% of the time**.\n",
    "\n",
    "In real life, we don't have the luxury of simulating the same experiment with multiple datasets. We often only have one. But we can draw on the intuition above to construct what we call **confidence intervals**. Confidence intervals come with a probability attached to them. The most common one is 95%. This probability tells us how many hypothetical confidence intervals we would build from different studies contain the true mean. For example, the 95% confidence intervals computed from similar studies would include the true mean 95% of the time. \n",
    "\n",
    "To calculate the confidence interval, we use the **central limit theorem**. This theorem states that **means of experiments are normally distributed**. From statistical theory, we know that 95% of the mass of a normal distribution is between 2 standard deviations above and below the mean. Technically, 1.96, but 2 is close enough. \n",
    "\n",
    "![normal_density](./data/img/stats-review/normal_dist.jpeg)\n",
    "\n",
    "The Standard Error of the mean serves as our estimate of the distribution of the experiment means. So, if we multiply it by 2 and add and subtract it from the mean of one of our experiments, we will construct a 95% confidence interval for the true mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(73.82718114045632, 74.17341543460314)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(321)\n",
    "exp_data = run_experiment()\n",
    "exp_se = exp_data.std() / np.sqrt(len(exp_data))\n",
    "exp_mu = exp_data.mean()\n",
    "ci = (exp_mu - 2 * exp_se, exp_mu + 2 * exp_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we don't need to restrict ourselves to the 95% confidence interval. We could generate the 99% interval by finding what we need to multiply the standard deviation by so the interval contains 99% of the mass of a normal distribution. \n",
    "\n",
    "The function `ppf` in python gives us the inverse of the CDF. Instead of multiplying the standard error by 2 like we did to find the 95% CI, we will multiply it by `z`, which will result in the 99% CI. So, `ppf(0.5)` will return 0.0, saying that 50% of the mass of the standard normal distribution (mean 0 and 1 standard deviation) is below 0.0. By the same token, if we plug 99.5%, we will have the value `z`, such that 99.5% of the distribution mass falls below this value. In other words, 0.5% of the mass falls above this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5758293035489004\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(73.7773381773405, 74.22325839771896)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "z = stats.norm.ppf(.995)\n",
    "print(z)\n",
    "ci = (exp_mu - z * exp_se, exp_mu + z * exp_se)\n",
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"99% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Back to our classroom experiment, we can construct the confidence interval for the mean exam score for both the online and face to face students' group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for Online: (70.56094429049804, 76.7095818797147)\n",
      "95% for Face to Face: (76.80278229206951, 80.29218687459715)\n"
     ]
    }
   ],
   "source": [
    "def ci(y: pd.Series):\n",
    "    return (y.mean() - 2 * se(y), y.mean() + 2 * se(y))\n",
    "\n",
    "print(\"95% CI for Online:\", ci(online))\n",
    "print(\"95% for Face to Face:\", ci(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the 95% CI of the groups doesn't overlap. The lower end of the CI for Face to Face class is above the upper end of the CI for online classes. This is evidence that our result is not by chance and that the true mean for students in face-to-face classes is higher than the true mean for students in online classes. In other words, there is a significant causal decrease in academic performance when switching from face-to-face to online classes.\n",
    "\n",
    "To recap, confidence intervals are a way to place uncertainty around our estimates. The smaller the sample size, the larger the standard error, and the wider the confidence interval. Since they are super easy to compute, lack of confidence intervals signals either some bad intentions or simply lack of knowledge, which is equally concerning. Finally, you should always be suspicious of measurements without any uncertainty metric. \n",
    "\n",
    "![img](data/img/stats-review/ci_xkcd.png)\n",
    "\n",
    "One final word of caution here. Confidence intervals are trickier to interpret than at first glance. For instance, I **shouldn't** say that this particular 95% confidence interval contains the true population mean with 95% chance. In frequentist statistics that use confidence intervals, the population mean is regarded as a true population constant. So it either is or isn't in our particular confidence interval. In other words, our specific confidence interval either contains or doesn't contain the true mean. If it does, the chance of containing it would be 100%, not 95%. If it doesn't, the chance would be 0%. Instead, in confidence intervals, the 95% refers to the frequency that such confidence intervals, computed in many studies, contain the true mean. 95% is our confidence in the algorithm used to calculate the 95% CI, not on the particular interval itself.\n",
    "\n",
    "Now, having said that, as an Economist (statisticians, please look away now), I think this purism is not very useful. In practice, you will see people saying that the particular confidence interval contains the true mean 95% of the time. Although wrong, this is not very harmful, as it still places a precise degree of uncertainty in our estimates. Moreover, if we switch to Bayesian statistics and use probable intervals instead of confidence intervals, we would be able to say that the interval contains the distribution mean 95% of the time. Also, from what I've seen in practice, with decent sample sizes, bayesian probability intervals are more similar to confidence intervals than Bayesian, and frequentists would like to admit. So, if my word counts for anything, feel free to say whatever you want about your confidence interval. I don't care if you say they contain the true mean 95% of the time. Please never forget to place them around your estimates; otherwise, you will look silly. \n",
    "\n",
    "\n",
    "## Hypothesis Testing\n",
    "\n",
    "Another way to incorporate uncertainty is to state a hypothesis test: is the difference in means statistically different from zero (or any other value)? We will recall that the sum or difference of 2 independent normal distributions is also normal distribution. The resulting mean will be the sum or difference between the two distributions, while the variance will always be the sum of the variance:\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) - N(\\mu_2, \\sigma_2^2) = N(\\mu_1 - \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) + N(\\mu_2, \\sigma_2^2) = N(\\mu_1 + \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "If you don't recall, its OK. We can always use code and simulated data to check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "n1 = np.random.normal(4, 3, 30000)\n",
    "n2 = np.random.normal(1, 4, 30000)\n",
    "n_diff = n2 - n1\n",
    "sns.distplot(n1, hist=False, label=\"$N(4,3^2)$\")\n",
    "sns.distplot(n2, hist=False, label=\"$N(1,4^2)$\")\n",
    "sns.distplot(n_diff, hist=False, label=f\"$N(1,4^2) - (4,3^2) = N(-3, 5^2)$\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we take the distribution of the means of our 2 groups and subtract one from the other, we will have a third distribution. The mean of this final distribution will be the difference in the means, and the standard deviation of this distribution will be the square root of the sum of the standard deviations.\n",
    "\n",
    "$\n",
    "\\mu_{diff} = \\mu_1 - \\mu_2\n",
    "$\n",
    "\n",
    "$\n",
    "SE_{diff} = \\sqrt{SE^2_1 + SE^2_2} = \\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}\n",
    "$\n",
    "\n",
    "Let's return to our classroom example. We will construct this distribution of the difference. Of course, once we have it, building the 95% CI is straightforward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-8.376410208363385, -1.4480327880905248)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "ci = (diff_mu - 1.96*diff_se, diff_mu + 1.96*diff_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(diff_mu - 4*diff_se, diff_mu + 4*diff_se, 100)\n",
    "y = stats.norm.pdf(x, diff_mu, diff_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=.05)\n",
    "plt.vlines(ci[0], ymin=0, ymax=.05, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this at hand, we can say that we are 95% confident that the true difference between the online and face-to-face groups falls between -8.37 and -1.44. We can also construct a **z statistic** by dividing the difference in mean by the $SE$ of the differences.\n",
    "\n",
    "$\n",
    "z = \\dfrac{\\mu_{diff} - H_{0}}{SE_{diff}} = \\dfrac{(\\mu_1 - \\mu_2) - H_{0}}{\\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}}\n",
    "$\n",
    "\n",
    "Where $H_0$ is the value which we want to test our difference against.\n",
    "\n",
    "The z statistic is a measure of how extreme the observed difference is. We will use contradiction to test our hypothesis that the difference in the means is statistically different from zero. We will assume that the opposite is true; we will assume that the difference is zero. This is called a null hypothesis, or $H_0$. Then, we will ask ourselves, \"is it likely that we would observe such a difference if the true difference were zero?\" We can translate this question to checking how far from zero is our z statistic in statistical math terms. \n",
    "\n",
    "Under $H_0$, the z statistic follows a standard normal distribution. So, if the difference is indeed zero, we would see the z statistic within 2 standard deviations of the mean 95% of the time. The direct consequence is that if z falls above or below 2 standard deviations, we can reject the null hypothesis with 95% confidence.\n",
    "\n",
    "Let's see how this looks like in our classroom example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.7792810791031224\n"
     ]
    }
   ],
   "source": [
    "z = diff_mu / diff_se\n",
    "print(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4,4,100)\n",
    "y = stats.norm.pdf(x, 0, 1)\n",
    "plt.plot(x, y, label=\"Standard Normal\")\n",
    "plt.vlines(z, ymin=0, ymax=.05, label=\"Z statistic\", color=\"C1\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks like a pretty extreme value. Indeed, it is above 2, which means there is less than a 5% chance that we would see such an extreme value if there were no difference in the groups. This again leads us to conclude that switching from face-to-face to online classes causes a statistically significant drop in academic performance.\n",
    "\n",
    "One final interesting thing about hypothesis tests is that it is less conservative than checking if the 95% CI from the treated and untreated group overlaps. In other words, if the confidence intervals in the two groups overlap, it can still be the case that the result is statistically significant. For example, let's pretend that the face-to-face group has an average score of 80 with a standard error of 4, and the online group has an average score of 71 with a standard error of 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control 95% CI: (67.08, 74.92)\n",
      "Test 95% CI: (72.16, 87.84)\n",
      "Diff 95% CI: (0.23461352820082482, 17.765386471799175)\n"
     ]
    }
   ],
   "source": [
    "cont_mu, cont_se =  (71, 2)\n",
    "test_mu, test_se = (80, 4)\n",
    "\n",
    "diff_mu = test_mu - cont_mu\n",
    "diff_se = np.sqrt(cont_se**2 + test_se**2)\n",
    "\n",
    "print(\"Control 95% CI:\", (cont_mu-1.96*cont_se, cont_mu+1.96*cont_se))\n",
    "print(\"Test 95% CI:\", (test_mu-1.96*test_se, test_mu+1.96*test_se))\n",
    "print(\"Diff 95% CI:\", (diff_mu-1.96*diff_se, diff_mu+1.96*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we construct the confidence intervals for these groups, they overlap. The upper bound for the 95% CI of the online group is 74.92, and the lower bound for the face-to-face group is 72.16. However, once we compute the 95% confidence interval for the difference between the groups, we can see that it does not contain zero. Even though the individual confidence intervals overlap, the difference can still be statistically different from zero.\n",
    "\n",
    "## P-values\n",
    "\n",
    "Previously, I've said that there is less than a 5% chance we would observe such an extreme value if the difference between online and face-to-face groups were actually zero. But can we precisely estimate what that chance is? How likely are we to observe such an extreme value? Enters p-values!\n",
    "\n",
    "Like with confidence intervals (and most frequentist statistics, as a matter of fact), the true definition of p-values can be very confusing. So, to not take any risks, I'll copy the definition from Wikipedia: \"the p-value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct\". \n",
    "\n",
    "To put it more succinctly, the p-value is the probability of seeing such data, given that the null hypothesis is true. It measures how unlikely it is that you are seeing a measurement if the null hypothesis is true. Naturally, this often gets confused with the probability of the null hypothesis being true. Note the difference here. The p-value is NOT $P(H_0|data)$, but rather $P(data|H_0)$.\n",
    "\n",
    "But don't let this complexity fool you. In practical terms, they are pretty straightforward to use.\n",
    "\n",
    "![p_value](./data/img/stats-review/p_value.png)\n",
    "\n",
    "To get the p-value, we need to compute the area under the standard normal distribution before or after the z statistic. Fortunately, we have a computer to do this calculation for us. We can simply plug the z statistic in the CDF of the standard normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value: 0.0027239680835563383\n"
     ]
    }
   ],
   "source": [
    "print(\"P-value:\", stats.norm.cdf(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the p-value is interesting because it avoids us having to specify a confidence level, like 95% or 99%. But, if we wish to report one, from the p-value, we know precisely at which confidence our test will pass or fail. For instance, with a p-value of 0.0027, we see that we have significance up to the 0.2% level. So, while the 95% CI and the 99% CI for the difference will neither contain zero, the 99.9% CI will. This means that there is only a 0.2% chance of observing this extreme z statistic if the difference was zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI: (-8.376346553082909, -1.4480964433710017)\n",
      "99% CI: (-9.46485353526404, -0.3595894611898709)\n",
      "99.9% CI: (-10.728040658245558, 0.9035976617916459)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "print(\"95% CI:\", (diff_mu - stats.norm.ppf(.975)*diff_se, diff_mu + stats.norm.ppf(.975)*diff_se))\n",
    "print(\"99% CI:\", (diff_mu - stats.norm.ppf(.995)*diff_se, diff_mu + stats.norm.ppf(.995)*diff_se))\n",
    "print(\"99.9% CI:\", (diff_mu - stats.norm.ppf(.9995)*diff_se, diff_mu + stats.norm.ppf(.9995)*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key Ideas\n",
    "\n",
    "We've seen how important it is to know Moivre’s equation, and we used it to place a degree of certainty around our estimates. Namely, we figured out that online classes cause a decrease in academic performance compared to face-to-face classes. We also saw that this was a statistically significant result. We did it by comparing the Confidence Intervals of the means for the 2 groups, looking at the confidence interval for the difference, doing a hypothesis test, and looking at the p-value. Let's wrap everything up in a single function that makes A/B testing comparison like the one we did above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.54748458333333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226955 +- 3.4641250548559537\n",
      "Z Statistic -2.7792810791031224\n",
      "P-Value 0.0027239680835563383\n"
     ]
    }
   ],
   "source": [
    "def AB_test(test: pd.Series, control: pd.Series, confidence=0.95, h0=0):\n",
    "    mu1, mu2 = test.mean(), control.mean()\n",
    "    se1, se2 = test.std() / np.sqrt(len(test)), control.std() / np.sqrt(len(control))\n",
    "    \n",
    "    diff = mu1 - mu2\n",
    "    se_diff = np.sqrt(test.var()/len(test) + control.var()/len(control))\n",
    "    \n",
    "    z_stats = (diff-h0)/se_diff\n",
    "    p_value = stats.norm.cdf(z_stats)\n",
    "    \n",
    "    def critical(se): return -se*stats.norm.ppf((1 - confidence)/2)\n",
    "    \n",
    "    print(f\"Test {confidence*100}% CI: {mu1} +- {critical(se1)}\")\n",
    "    print(f\"Control {confidence*100}% CI: {mu2} +- {critical(se2)}\")\n",
    "    print(f\"Test-Control {confidence*100}% CI: {diff} +- {critical(se_diff)}\")\n",
    "    print(f\"Z Statistic {z_stats}\")\n",
    "    print(f\"P-Value {p_value}\")\n",
    "        \n",
    "AB_test(online, face_to_face)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our function is generic enough, we can test other null hypotheses. For instance, can we try to reject that the difference between online and face-to-face class performance is -1? With the results we get, we can say with 95% confidence that the difference is more significant than -1. But we can't say it with 99% confidence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.54748458333333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226955 +- 3.4641250548559537\n",
      "Z Statistic -2.2134920404560883\n",
      "P-Value 0.013431870694630114\n"
     ]
    }
   ],
   "source": [
    "AB_test(online, face_to_face, h0=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "I like to think of this entire book as a tribute to Joshua Angrist, Alberto Abadie and Christopher Walters for their amazing Econometrics class. Most of the ideas here are taken from their classes at the American Economic Association. Watching them is what is keeping me sane during this tough year of 2020.\n",
    "* [Cross-Section Econometrics](https://www.aeaweb.org/conference/cont-ed/2017-webcasts)\n",
    "* [Mastering Mostly Harmless Econometrics](https://www.aeaweb.org/conference/cont-ed/2020-webcasts)\n",
    "\n",
    "I'll also like to reference the amazing books from Angrist. They have shown me that Econometrics, or 'Metrics as they call it, is not only extremely useful but also profoundly fun.\n",
    "\n",
    "* [Mostly Harmless Econometrics](https://www.mostlyharmlesseconometrics.com/)\n",
    "* [Mastering 'Metrics](https://www.masteringmetrics.com/)\n",
    "\n",
    "My final reference is Miguel Hernan and Jamie Robins' book. It has been my trustworthy companion in the most thorny causal questions I had to answer.\n",
    "\n",
    "* [Causal Inference Book](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/)\n",
    "\n",
    "The data used here is from a study of Alpert, William T., Kenneth A. Couch, and Oskar R. Harmon. 2016. [\"A Randomized Assessment of Online Learning\"](https://www.aeaweb.org/articles?id=10.1257/aer.p20161057). American Economic Review, 106 (5): 378-82.\n",
    "\n",
    "![img](./data/img/poetry.png)\n",
    "\n",
    "## Contribute\n",
    "\n",
    "Causal Inference for the Brave and True is an open-source material on causal inference, the statistics of science. Its goal is to be accessible monetarily and intellectually. It uses only free software based on Python.\n",
    "If you found this book valuable and want to support it, please go to [Patreon](https://www.patreon.com/causal_inference_for_the_brave_and_true). If you are not ready to contribute financially, you can also help by fixing typos, suggesting edits, or giving feedback on passages you didn't understand. Go to the book's repository and [open an issue](https://github.com/matheusfacure/python-causality-handbook/issues). Finally, if you liked this content, please share it with others who might find it helpful and give it a [star on GitHub](https://github.com/matheusfacure/python-causality-handbook/stargazers)."
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